Infinity is not an "isness" in that an infinite amount of anything can exist at one time. But time, as far as we know, is indivisible; one can take a second and divide that moment forever, ergo that single second is infinite. Also in the multi-universe model all universes don't have to exist now and all possible universes will never exist, but infinity does not require every combination, only continuity.

the number line between 0 and 1 has length 1
- to find out how many things fit on the line
- divide line length by the thing length
- a number has length 0
- so the number of number between 0 and 1 is 1/0=UNDEFINED
- if you let number have non-zero length then there is a finate number of numbers in the interval but a potential infinity as number length tends to zero — Devans99

This is what happens when you don't understand math. At all. I mean, it's almost like numbers such as 0.5 exist.

I can’t believe you; we’ve been talking about this for ages and you have learned nothing. You are still not even using the proper language to discuss this is (actual/potential infinity). — Devans99

Aside from people who insist on stupid Aristotelian terms, only Intuitionists sort of use those terms, but even they accept that at least one infinite set exists (the naturals). You're not using the "proper language", you read some Aristotle (or more likely a summary of bits of him) and parade it around like a Randian does their political philosophy. You haven't even understood how this discussion is actually done in the last century and a half.

You need to realise that you were told the wrong things about infinity at school and free your mind of Cantor’s muddled dogma. — Devans99

HAHAHAHAHAHA.

No really, I'm done this time. I know I've said it repeatedly, but you were kind enough to finally be explicit about what you believed. Have fun pretending to be talking about "Cantor's dogma" while ignoring everything required to understand his work and the work that came after.

Clearly, for any set of natural numbers, a proper subset is always smaller. That is always the case, and there is never an exception. — Metaphysician Undercover

This is what happens when you don't realize that Even numbers exist, are a proper subset of the naturals, and are provably the same size as the naturals.

0 - 0
1 - 2
2 - 4
3 - 6

If the even numbers (those on the right side) are smaller (as you say proper subsets "clearly are") then point out exactly when the even numbers fail to give a number to match to the naturals. If you can't do that (which you can't) then the only way you can continue is by ignoring the definitions used. So I'm just not bothering anymore.

We have been discussing this here:

https://thephilosophyforum.com/discussion/4073/do-you-believe-in-the-actually-infinite/p1

I think most people are in agreement with you.

I don't totally follow your argument, perhaps you expand...

This thread has been restored from the inadvertent closure that happened to it. Anybody that wants to post in it should now find it possible to do so.

Here are two of the typical arguments against an infinite past, and why they don't hold up. (Some basic mathematics required.)

Last Thursdayism

• Assumption (towards reductio ad absurdum): infinite temporal past
• Let's enumerate past days up to and including last Wednesday as: {..., t, ..., -1, 0}
  That is, there exists a bijection among those past days (including Wednesday) and the non-positive integers
• Now come Thursday
• Observation: {..., t, ..., -1, 0} cannot accommodate Thursday
• Let's re-enumerate the same past days but including Thursday as: {..., t, ..., -1, 0}
  That is, there exists a bijection among those past days (including Thursday) and the non-positive integers
• Observation: {..., t, ..., -1, 0} can accommodate Thursday
• The two observations are contradictory
• {..., t, ..., -1, 0} both cannot and can accommodate Thursday
• Conclusion: the assumption is wrong, an infinite past is impossible

This argument could equally be applied to infinite causal chains, and nicely lends support to the Omphalos hypothesis (hence why I named it Last Thursdayism). Another thing to notice about the infinite set of integers: any two numbers are separated by a number. And this number is also a member of the integers. That is, the integers are closed under subtraction and addition. For the analogy with enumerating past days, this means any two events are separated by a number of days. Not infinite, but a particular number of (possibly fractional) days. That's any two events. To some folk this is counter-intuitive, but, anyway, there you have it.

The first observation is incorrect. Whether or not the set can accommodate Thursday (one more day), is not dependent on one specific bijection (the first selected), rather it is dependent on the existence of some (any such) bijection. A bijection also exists among {..., t, ..., -1, 0} and {..., t, ..., -1, 0, 1}, and the integers, for that matter.

Therefore, the argument is not valid.

The unnumbered now

1. if the universe was temporally infinite, then there was no 1^st moment
2. if there was no 1st moment (but just some moment), then there was no 2^nd moment
3. if there was no 2nd moment (but just some other moment), then there was no 3^rd moment
4. ... and so on and so forth ...
5. if there was no 2^nd last moment, then there would be no now
6. since now exists, we started out wrong, i.e. the universe is not temporally infinite

The argument shows that, on an infinite temporal past, the now doesn't have a definite, specific number, as per 1^st, 2^nd, 3^rd, ..., now. Yet, we already knew this in case of an infinite temporal past, so, by implicitly assuming otherwise, the argument can be charged with petitio principii.

Additionally, note that 1,2,3 refer to non-indexical "absolute" moments (1^st, 2^nd, 3^rd), but 5 is indexical and contextual (2^nd last, now), which is masked by 4. We already know from elsewhere (originating in linguistics) that such reasoning is problematic.

That is, 6 is a non sequitur, and could be expressed more accurately as:

5. if there was no 2^nd last moment with an absolute number, then there would be no now with an absolute number
6. since now exists, we started out wrong, i.e. any now does not have an absolute number


Hilbert's Hotel and Shandy's Diary, for example, are peripherally related, known veridical paradoxes, and do not imply a contradiction, but they do show some counter-intuitive implications of infinites.

However, completing an infinite process is not a matter of starting at a particular time that just happens to be infinitely far to the past and then stopping in the present. It’s to have always been doing something and then stopping. This point is illustrated by a possibly apocryphal story attributed to the philosopher Ludwig Wittgenstein. Imagine meeting a woman in the street who says, “Five, one, four, one, dot, three! Finally finished!” When we ask what is finished, she tells us that she just finished counting down the infinite digits of pi backward. When we ask when she started, she tells us that she never started, she has always been doing it. The point of the story seems to be that impossibility of completing such an infinite process is an illusion created by our insistence that every process has a beginning. — James Harrington

• Time: A Philosophical Introduction

There is no logical or conceptual barrier to the notion of infinite past time.
In a lecture Wittgenstein told how he overheard a man saying '...5, 1, 4, 1, 3, finished'. He asked what the man had been doing.
'Reciting the digits of Pi backward' was the reply. 'When did you start?' Puzzled look. 'How could I start. That would mean beginning with the last digit, and there is no such digit. I never started. I've been counting down from all eternity'.
Strange, but not logically impossible. — Craig Skinner

• Pathways to Philosophy - Ask a Philosopher: Questions and Answers 47 (2^nd series), question 94

∞ does not derive a contradiction, rather, to learn more about our world, we'll have to go by evidence and try to piece things together.


_{Whitrow and Popper on the impossibility of an infinite past by William Lane Craig
Georg Cantor (1845-1918): The man who tamed infinity by Eric Schechter}

Hilbert's Hotel and Shandy's Diary, for example, are peripherally related, known veridical paradoxes, and do not imply a contradiction, — jorndoe

"contradiction, noun, a combination of statements, ideas, or features which are opposed to one another."

A completely full hotel that can except infinity many new guests is definitely contradictory.

This is what happens when you don't realize that Even numbers exist, are a proper subset of the naturals, and are provably the same size as the naturals.

0 - 0
1 - 2
2 - 4
3 - 6

If the even numbers (those on the right side) are smaller (as you say proper subsets "clearly are") then point out exactly when the even numbers fail to give a number to match to the naturals. If you can't do that (which you can't) then the only way you can continue is by ignoring the definitions used. So I'm just not bothering anymore. — MindForged

Clearly, your sets as written do not indicate that the right is a subset of the left. The left contains 4 and 6, which are not contained in the right. It is not a subset.

There is a set X having the property that ∅ is an element of X, and whenever x is an element of X, then x∪{x} is also an element of X.

This is a very precise formulation which one can show yields a set which is not finite (hence infinite):

As ∅ is in X, then ∅∪{∅}={∅} is an element of X.
As {∅} is in X, then {∅}∪{{∅}}={∅,{∅}} is in X.
As {∅,{∅}} is in X, then {∅,{∅}}∪{{∅,{∅}}}={∅,{∅},{∅,{∅}}} is in X.
...
You see that these elements of X get larger and larger without (finite) bound, and so it stands to reason that such an X must be infinite. — tim wood

I don't see how this proves that n infinite set is possible. It seems to assume that an infinite set is possible, "begs the question". Could you provide a rendition in English?

'When did you start?' Puzzled look. 'How could I start. That would mean beginning with the last digit, and there is no such digit. I never started. I've been counting down from all eternity' — Craig Skinner

I think you might be over complicating things. Things without a start don't exist:

- X exists eternally within time
- So X has no temporal start
- So X does not exist

So nothing can be eternal within time. What about time itself, does that have a start? If you believe in Relativity/Eternalism then time is a real, persistent 'thing' so it has a start. So presumably you are a Presentist? That leads to other paradoxes; you might want to comment on this thread:

https://thephilosophyforum.com/discussion/4158/nine-nails-in-the-coffin-of-presentism/p1

- Assume space is continuous
- Then there is an actually infinite amount of information in a spacial volume of 10000 cubic units
- There is also an actually infinite amount of information in a spacial volume of 1 cubic unit
- Both infinities have the same cardinality so maths says they are the same size
- But this is a logical contradiction, there must be more information in the larger volume.
- So space must be discrete or maths treatment of infinity is wrong (or both probably)

Same argument for time...

"contradiction, noun, a combination of statements, ideas, or features which are opposed to one another." — Devans99

Or more formally put, for a proposition p, p ∨ ¬p is a contradiction.

A completely full hotel that can except infinity accept infinitely many new guests is definitely contradictory. — Devans99

If we're talking an ordinary full hotel, yes, which isn't the case here, hence the counter-intuitive nature of ∞.

(Some basic mathematics required.) — jorndoe

First we need to set up what infinite past means. It means there are an infinite number of events have occurred before the present. My first point is all events in that situation would have to be real. Second is if such was, than each event from the present can be represented by a number, for example event 1 would be the event that just occurred before present and event 2 would be the event that just occurred before event one and as such to infinity.

All events in that past must have been the present at one point. If we designate the present as a point, then all points after that would be a finite amount. Since all events are numbered from the present, let's say that we ask "how many events that are even numbered and we would say infinity. Since that represents real events than there must be an event in the past that is infinite events away for even+odd=total of any number event. This is not possible for such an event would have been the present and as such can not be for that means the current present happened if an infinite number of events occurred and an addition synthesis to infinity from finite set is impossible.

I think you're missing something here. There cannot be an event #1, because as soon as it occurs it's in the past, replaced by another event. This jeopardizes your premise "all events in that past must have been the present at one point."

Any event takes time, so by the end of the event, the beginning is already in the past. This means that any event is divisible. We can divide it into the part which has already occurred, and the part which has not yet occurred. But if we allow that there is a part which is occurring, then this itself is divisible into the part occurred and the part not yet occurred. So if the part which is occurring, is the present, the present cannot be a point because the occurrence itself, what is occurring, is what is at the present, and this is always divisible, unlike the point. And if we divide it as if at a point, then part is in the future, and part is in the past but none of the event is at the present, which is just a point.

Time itself as a measurement is relative because measurement are by itself comparing another event. Like a second is "9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium" atom. A phenomenon is either happened or would be happening. The present is the last phenomenon that just occurred and if we use time by just relative to what happened that the present is the instaneous point where A just occurred. This means my point of the past is the events that occur in succession before the point now. Now by definition is what is here at the moment and A just happened therefore my argument still is true for no infinite number of events can occur after after A, which from my previous post, I said that every past event must have been that instantaneous point of occurance that just happened. If there was an infinite past, than an event that is an infinite number of events from the present occured but that is impossible for an addition synthesis to infinity with a finite set like A1 A2 ... etc. Etc. .Your point seems to conflate that the present is occured and occurring which is not. What has just occured becomes different depending on the relative measurement from something new.

Simple visual is A is the present and events after it are called A1, A2, A3 ... and so on. There can not be an infinite number of events after A because addition synthesis does not lead to infinity

Same would apply to the claim that an infinite past is possible forgets that the past is all events that were the instantaneous event that occured and was a that point what is like one moment you have A green fire and at that instant that was the present and than a blue came after it.

What is the present changes but the events in the last was the present and since the total amount of anything is even+odd than the amount of even numbered events before an instanceous present is infinity. Which means that an event infinite events from the present was the present but that means the present now came an infinite events which would be impossible for an addition synthesis is impossible.

The present is the last phenomenon that just occurred and if we use time by just relative to what happened that the present is the instaneous point where A just occurred. — BB100

You are creating an artificial discontinuity. There is no real point when A ends. If A, B, and C, are a series of events, there is continuity between them such that any ending of A and beginning of B is a function of the description. We describe things as one event ending, and the next beginning, but in reality there is continuity between them such that the point where one ends and the next begins is arbitrary.

If you start counting from the end of event A, your count is completely arbitrary. You are not counting anything real, you are counting properties of your description. If you cannot demonstrate that such "points" are real, there is nothing to indicate that your count is nothing more than fiction. If time is continuous, as it appears to be, then the past is just one big event. If that event continues at the present, then you cannot put an arbitrary end to it, at the present, because this is a false representation.

Simple visual is A is the present and events after it are called A1, A2, A3 ... and so on. There can not be an infinite number of events after A because addition synthesis does not lead to infinity — BB100

Again, your representation of the present, as a point, is not supported by any firm ontology, as the passing of time is considered to be continuous. So any representations, or conclusions, you derive from this are meaningless fiction.

as the passing of time is considered to be continuous — Metaphysician Undercover

I was wondering about that: If time is truly continuous then a 1 second interval is graduated as finely as a 1 hour interval (implicit from the definition of continuous). That seems contradictory by itself: suggests the short interval contains as many distinct states (therefore information) as the long interval...

I was wondering about that: If time is truly continuous then a 1 second interval is graduated as finely as a 1 hour interval (implicit from the definition of continuous). That seems contradictory by itself: suggests the short interval contains as many distinct states (therefore information) as the long interval... — Devans99

That's the consequence of assuming infinite divisibility of the continuous. A 1 second interval is infinitely divisible, as is a 1 hour interval. It's the same issue as the real numbers.

The contradiction is in the assumption that the continuous is divisible. If you can really divide it, then it is not continuous, as per the divisions. If it is really continuous then you can't really divide it as that would make it discontinuous. So there is a separation between the continuous thing, and the divisions which we assign to it.

The continuous thing, being time as it exists passing in the world, is not really separated by those divisions, which we assign to it. The divisions, a second, an hour, etc., are within our descriptions, not within the continuous thing, making a categorical separation between the two, such that we are not really dividing the thing. The divisions are conceptual only, used to facilitate understanding of the thing described, like coordinates of a map.

as the passing of time is considered to be continuous — Metaphysician Undercover
I was wondering about that: If time is truly continuous then a 1 second interval is graduated as finely as a 1 hour interval (implicit from the definition of continuous). That seems contradictory by itself: suggests the short interval contains as many distinct states (therefore information) as the long interval... — Devans99

Lets consider the points on the interval 0 to 1 on the x axis. Assume a point is just a location on the interval and the point itself has zero width on the interval. Now consider the usual setup where we put a bunch of these points on the interval and separate them by dx. As long as dx is not zero the number of points will be discrete and they will not count to Infinity. Remember that a differential dx only approaches Zero. If dx = 0 then there will be Infinite points but you cannot arrange points with Zero width along side each other when dx = 0. They will all have to superimpose on top of each other and the whole x axis of points will collapse on top of the point x=0. This is just nonsense and shows that trying to use actual Infinity as a real quantity of anything is not possible. Mathematicians always say things only approach Infinity. Infinity is a Mathematical fiction. It is a goal that cannot be achieved. Mathematics breaks down when faced with Infinity. Cantor used the slight of hand talking about Countable Infinities as if such a thing was not a contradiction. Don't be fooled. There is no such a thing as an Infinite anything. There can be no actual Infinite Information in any volume. The moment the Information would become Infinite then the dV = 0. So each differential Volume would have to be identically Zero for Infinite Information. An Infinite amount of Zero is still zero. Infinity is a nonsensical concept to begin with.

The contradiction is in the assumption that the continuous is divisible. If you can really divide it, then it is not continuous, as per the divisions. If it is really continuous then you can't really divide it as that would make it discontinuous — Metaphysician Undercover

But the continuous is by definition infinitely divisible:

https://en.wikipedia.org/wiki/Discrete_time_and_continuous_time

So infinitely divisible time gives an infinite number of states (and thus information) for any system over any finite time period. The same kind of infinity for all systems independent of their size. To me this contradiction points to discrete space and time.

Mathematicians always say things only approach Infinity — SteveKlinko

Unfortunately this is far from universally the case; many mathematicians have made a substantial intellectual investment in Cantor's flavour of actual infinity and are quite hostile to anyone questioning set theory's approach. There are also Cosmologists with models based on actual infinity for time and/or space who are not very open minded when the existence of actual infinity is questioned.

Mathematicians always say things only approach Infinity — SteveKlinko
Unfortunately this is far from universally the case; many mathematicians have made a substantial intellectual investment in Cantor's flavour of actual infinity and are quite hostile to anyone questioning set theory's approach. There are also Cosmologists with models based on actual infinity for time and/or space who are not very open minded when the existence of actual infinity is questioned. — Devans99

That's how it is when someone has a Belief about something. None of us can truly comprehend Infinity with our limited Human Brains. Every time you really work out a problem or analyze a little Deeper it is always found that Infinity is a big problem.

To the Metaphysician Undercover, Ot seems I will have to define tine more simple.

There can be two meanings of time, the measurement of events relative to others, and the description of each event in their order.

Measurement of time is simply saying that event x occurs after 3 events of y. An event is simply the description of phenonmen(that which is not and than is). These may not be divisible because by definition an event is or not and could only be measured with other events that would set on nature.

The other meaning of time is as I mentioned event A has a green fire than there us not, in such there are multiple phenomenon that have just happened but it being continuous is just based on humans perceived change in a certain order that makes it seem continuous. Like an old film that went really fast like 280 frames per second and could not tell it is set points of pictures in a certain order.

Divisiblity occurs because of the preconceived notion that space has points in between every line segment which does not work which change of a system.

That's how it is when someone has a Belief about something — SteveKlinko

The traditional Christian view of God is that he is eternal and infinite. I wonder if some people are still religiously invested in infinity? I suspect some atheists might likewise be 'religiously' invested in infinity as a mechanism to explain the apparent fine tuning of the universe for life?

Every time you really work out a problem or analyze a little Deeper it is always found that Infinity is a big problem — SteveKlinko

Wikipedia lists a few (but there are more):

https://en.wikipedia.org/wiki/List_of_paradoxes#Infinity_and_infinitesimals

In cosmology they have this paradox:

https://en.wikipedia.org/wiki/Measure_problem_(cosmology)

The solution is a finite universe but cosmologists press on regardless...

But the continuous is by definition infinitely divisible: — Devans99

That's contradictory, isn't it? If it were divided, it would not be continuous. The points and divisions exist in principle only. They are in the representation of time, the model of time, not in time itself. If time itself were thus divided it would not be continuous, it would be discrete. To avoid contradiction we could assume that time is discrete, but this is not how time appears to us, it appears to be continuous.

There can be two meanings of time, the measurement of events relative to others, and the description of each event in their order. — BB100

What about the thing which passes, as I sit here. That's how I understand time, not as a measurement of events, nor as a description of events, but what passes, and allows for events to occur.

That's contradictory, isn't it? If it were divided, it would not be continuous — Metaphysician Undercover

What I mean is you can divide continuous time to an infinite degree, so it can represent an infinite number of states, which equates to infinite information content.

If you imagine a system evolving through an infinite number of states over a finite period of time; each state is information (from the 4d space time perspective) so the system over the finite time period is described by infinite states thus infinite information.

I'll try to put it another way:

The Continuum can be modelled by the real numbers between 0 and 1. So that means any moment in the Continuum is represented by a decimal with infinite precision = infinite bits of information.

The Continuum for 1 second of time is identical to the Continuum for 1 year of time in that they are both described by the reals between 0 and 1. So 1 second and 1 year have the same information content. Hence the contradiction. Hence time should be discrete.

In contrast, a discrete second of time can be modelled with the natural numbers between 0 and some finite N. Then 1 second contains N possible states, but 1 year contains N*60*60*24*365 possible states; hence no contraction for discrete time.

but this is not how time appears to us, it appears to be continuous. — Metaphysician Undercover

Any discreteness in time would manifest somewhere down near Planck Time so we'd probably never be able to tell. Matter seems discrete at sub-atomic level. I suspect space-time is too?

Metaphysician Undercover, that which you say passes means your comparing one event with another which is what a measurement is, to compare like with other like. One event is just a description of phenomenon at such point. If you have that which differs than that is in its own event. Time is not divisible for that means it made out of parts, but time is that which happens. This means that any change is just a happening that when observed appears to be from this than there are points in between. But that would mean another event, not one that is part of this.

What I mean is you can divide continuous time to an infinite degree, so it can represent an infinite number of states, which equates to infinite information content. — Devans99

What I mean, is that you're not really dividing the time itself. We say that there are sixty minutes in an hour, sixty seconds in a minute, and so on, but time passes in the exact same way, whether you are counting minutes or seconds, because you are not really dividing the time, you are just counting it, and you may count fast or slow.

If you imagine a system evolving through an infinite number of states over a finite period of time... — Devans99

Actually, I can't imagine such a thing, it appears to be impossible. If you could have a finite period of time, it would be impossible to have an infinite number of states in that time because it would require time to change from one state to the next. Since there is a finite period of time, there could only be a finite number of changes between states, and therefore a finite number of states.

The Continuum can be modelled by the real numbers between 0 and 1. — Devans99

I don't believe that you can model a continuum in this way, because you are assigning ends to it. What principle allows you to put a beginning and an end to a continuum? This would make it into a discrete unit.

The Continuum for 1 second of time is identical to the Continuum for 1 year of time in that they are both described by the reals between 0 and 1. So 1 second and 1 year have the same information content. Hence the contradiction. Hence time should be discrete. — Devans99

This is contradiction. You are saying that the continuum is made up of discrete units, "1 second", "1 year". To say that is to deny that it is a continuum.

In contrast, a discrete second of time can be modelled with the natural numbers between 0 and some finite N. Then 1 second contains N possible states, but 1 year contains N*60*60*24*365 possible states; hence no contraction for discrete time. — Devans99

Right, if you could model time as discrete units you would not run into these problems. The problem though, is that we experience time as continuous, and we've found no natural divisions to form the basis for the finite N, the number of discrete units per second. I don't think the Planck unit provides us with this.

Metaphysician Undercover, that which you say passes means your comparing one event with another which is what a measurement is, to compare like with other like. — BB100

No, I'm not talking about comparing events, I'm talking about simply experiencing time passing. Have you ever sat and listened to music, or watched the sunset? Or maybe you like to meditate? It is not a matter of comparing events, nor describing events, it's just a matter of enjoying the wondrous "passing of time"

This means that any change is just a happening that when observed appears to be from this than there are points in between. But that would mean another event, not one that is part of this. — BB100

Suppose there are "points" in between passing time. How would this means that there are other events corresponding to these points? The points would be between the events, so there wouldn't be any time occurring at the points, nor events occurring at the points.

Watching a sunset means to observe a sun from one event being not below horizon to is one. Remember that is comparing and observation is a phenomenon therefore you are part of the event as well as thoughts that you think of. It's just comparing a prior to the now. Experiencing events occurring and thinking what replaced it, comparing by nature. Also when I mean points I meant if you were to describe a ball at the top of your house and than it was on your porch, it would be referring to the events that happened in between those two like being at certain relative distances at certain events. This also goes to my point of not infinite past for there can not be an infinite events inverween the ball at the top and to the prch for addition synthesis from a point never leads to infinity.